A simple receiver for linearly modulated sequence of symbols

From Tools4SDR

This page is a tutorial about a very simple receiver for linearly modulated sequences of symbols. It is based on the following pages:

• The software which send an image to generate the signal to process
• Tutorial on how to receive a signal
• Frequency offset estimation
• How to estimate the channel impulse response

Signal generation

As mentionned, we therefore use the The software which send an image to generate the signal to process

Note that you have to use the same training sequence file with the TX and with the RX.

Signal processing at the receiver

We assume that you have been able to receive a signal, correct its frequency offset, and perform the time synchronisation. These steps are described in the pages mentionned in the introduction. We just focus on the receiver part in this section.

As mentionned in the software page, the transmitter transmits data with the following structure:

We assume that you are synchronised with a given frame which correspond to index i0. As the signal is oversampled with a factor 5, you can estimate the channel impulse response of 5 signals:

1. Sig(i0+0:5:end)
2. Sig(i0+1:5:end)
3. Sig(i0+2:5:end)
4. Sig(i0+3:5:end)
5. Sig(i0+4:5:end)

For each frame, you can process as follows:

• Estimate the signal which is the best synchronised, i.e. the signal for which the channel impulse response is the closest to a Dirac.
• Estimate the channel impulse response
• Compensate the channel distorsions

Fine synchronisation

For each signal, you have a channel impulse response which is close to a Dirac if you are synchronised. The first step of the receiver is then the following one (for each frame): Select the signal which is the best synchronised.

Several options are possible to do that. You can either search for the channel which has only on significant value. Or you can test the kurtosis of the different signal. The best synchronised signal being the one which kurtosis is minimal.

Compensate the channel distorsions

Once you have selected this signal, the receiver then simply performs the compensation by dividing the received signal by the main coefficient of the estimated channel impulse response, and applying a delay which is the time delay for which the channel IR is maximal.

Results

The result of these treatments are the following ones. On the left, the variation over the frames of the channel impulse response of the first signal Sig(i0+0:5:end) is plotted. On the right, the received constellation at the output of the receiver.